Framework for personalization of coronary flow computations during rest and hyperemia

ABSTRACT

Embodiments relate to non-invasively determining coronary circulation parameters during a rest state and a hyperemic state for a patient. The blood flow in the coronary arteries during a hyperemic state provides a functional assessment of the patient&#39;s coronary vessel tree. Imaging techniques are used to obtain an anatomical model of the patient&#39;s coronary tree. Rest boundary conditions are computed based on non-invasive measurements taken at a rest state, and estimated hyperemic boundary conditions are computed. A feedback control system performs a simulation matching the rest state utilizing a model based on the anatomical model and a plurality of controllers, each controller relating to respective output variables of the coronary tree. The model parameters are adjusted for the output variables to be in agreement with the rest state measurements, and the hyperemic boundary conditions are accordingly adjusted. The hyperemic boundary conditions are used to compute coronary flow and coronary pressure variables.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. provisional application Ser.No. 61/611,210, filed Mar. 15, 2012, which is incorporated herein byreference in its entirety.

TECHNOLOGY FIELD

The present invention relates generally to determining coronarycirculation parameters for a patient, and more particularly to anon-invasive approach utilizing a feedback control system fordetermining coronary circulation parameters during a rest state and ahyperemic state for a patient.

BACKGROUND

Imaging results are typically used by physicians to diagnose conditionsand determine treatments related to a patient's coronary tree, such asblockages in various coronary vessels. For example, if a blockageappears to be serious, the physician may take invasive measures, such asstent insertion or surgery, to relieve the blockage. However, theimaging results alone often do not provide a complete assessment to thephysician. In particular, the imaging results do not provide afunctional assessment of the patient's coronary tree, which may bevaluable to the physician in the diagnosis and subsequent treatment. Itis thus desired to have a non-invasive approach for obtaining afunctional assessment of the patient's coronary tree.

SUMMARY

Embodiments of the present invention provide for the determination ofcoronary circulation parameters during a rest state and a hyperemicstate for a patient via non-invasive measurements and an iterativeparameter estimation framework based on a feedback control system. Thisnon-invasive approach allows for obtaining a functional assessment ofthe patient's coronary vessels.

According to an embodiment, determination of the coronary circulationparameters includes obtaining, via imaging, an anatomical model of acoronary tree of the patient; determining rest boundary conditions ofthe patient based on non-invasive measurements taken at a rest state;computing hyperemic boundary conditions of the patient; implementing afeedback control system to perform a simulation matching the rest state,wherein the feedback control system utilizes a model based on theanatomical model of the coronary tree and a plurality of controllers,each of the plurality of controllers relating to a respective outputvariable of the coronary tree, and wherein parameters of the model areadjusted for the output variables to be in agreement with the rest statemeasurements; adjusting the hyperemic boundary conditions based on theadjustments to the model; and performing a flow computationcorresponding to the hyperemic state using the adjusted model.

In an embodiment, the simulation corresponding to the hyperemic stateresults in hyperemic output variables of the coronary tree, thehyperemic output variables comprising one or more of coronary flow andcoronary pressure.

In an embodiment, the anatomical model of the coronary tree of thepatient is obtained via at least one of a CT scan, an MRI scan, anangiography scan, an ultrasound scan, and a cardiac perfusion scan.

According to an embodiment, the non-invasive measurements taken at arest state comprise one or more of heart rate, systolic blood pressure,and diastolic blood pressure.

In an embodiment, the rest boundary conditions of the patient compriseterminal resistance and capacitance values at vessel outlets during therest state. According to an embodiment, the rest boundary conditions areadjusted using information from a cardiac perfusion exam.

In an embodiment, the hyperemic boundary conditions of the patient are afunction of the rest boundary conditions of the patient and compriseterminal resistance values at vessel outlets during the hyperemic state.According to an embodiment, the hyperemic boundary conditions areadjusted using information from a cardiac perfusion exam.

In an embodiment, a first of the plurality of controllers relates tocoronary resistance of the coronary tree, and a second of the pluralityof controllers relates to cardiac output.

According to an embodiment, the model parameters are adjusted in aseries of iterations until the output variables are in agreement withthe measured patient data.

Additional features and advantages of the invention will be madeapparent from the following detailed description of illustrativeembodiments that proceeds with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other aspects of the present invention are bestunderstood from the following detailed description when read inconnection with the accompanying drawings. For the purpose ofillustrating the invention, there is shown in the drawings embodimentsthat are presently preferred, it being understood, however, that theinvention is not limited to the specific instrumentalities disclosed.Included in the drawings are the following figures.

FIG. 1 is an overview representation of a workflow for non-invasivelydetermining coronary circulation parameters during a hyperemic state fora patient, according to an embodiment;

FIG. 2 is a representation of the estimation of boundary conditions atthe rest state, according to an embodiment;

FIG. 3 is a representation of the estimation of boundary conditions atthe hyperemic state, according to an embodiment;

FIG. 4 is a block diagram representation of a feedback control systemthat is used for rest state simulation, according to an embodiment;

FIGS. 5A and 5B are flow charts illustrating the process of determiningthe coronary circulation parameters during the hyperemic state for apatient, according to an embodiment;

FIG. 6 is a representation of the coronary circulation system used invarious embodiments;

FIGS. 7A and 7B illustrate results of analyses for a test scenario ofaspects of the present invention; and

FIGS. 8A 8B, 8C, and 8D are a series of graphs illustrating coronarycirculation parameters during an example simulation, according to anembodiment.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Embodiments of the present invention relate to non-invasivelydetermining coronary circulation parameters during a rest state and ahyperemic state for a patient. The blood flow in the coronary arteriesduring a hyperemic state provides a functional assessment of thepatient's coronary tree, which serves as a valuable tool to a physicianfor diagnosis and treatment. The hyperemic state refers to a non-reststate in which the heart is pumping more blood than at the rest state.The non-invasive approach provided by embodiments of the presentinvention is desirable as the patient is not subjected to lengthy and/oruncomfortable invasive measures, which inherently have risks, such as,for example, infection.

According to embodiments, imaging results are used to provide ananatomical view or model of a patient's coronary vessels or coronarytree. The anatomical information provided by imaging includes suchfeatures as the size and location of blockage in the coronary tree. Inorder to determine how the anatomical information functionally affectsthe patient, embodiments of the present invention provide a method fordetermining the blood flow in the coronary arteries during a hyperemicstate. This method is based on a novel estimation procedure fordetermining boundary conditions from non-invasively acquired patientdata at rest. A multi-variable feedback control framework is utilized toensure that simulated parameter values, based on the anatomicalinformation provided by imaging, match the estimated values for anindividual patient during the rest state. The boundary conditions athyperemia are derived from the respective rest state values via atransfer function that is based on known physical characteristics andphenomena. The parameters that are the main determinants of coronaryblood flow during rest state are heart rate, average aortic pressure,and the myocardial mass, for example. Since these parameters (andconsequently the rest circulation) have a high variability betweenindividuals, the main coronary diagnostic indexes are based on thehyperemic blood flow conditions, which are specific to a particularpatient.

According to embodiments provided herein, the method may be summarizedas follows: first the rest boundary conditions are determined, followedby a computation of the hyperemic boundary conditions. Next, a feedbackcontrol system is used to perform a simulation that matches the reststate. Finally, after establishing the hyperemic boundary conditions,the arterial model is taken out of the control loop and a simulationcorresponding to the hyperemic state is performed.

FIG. 1 provides a high-level overview representation of the workflow 100for non-invasively determining coronary circulation parameters during ahyperemic state for a patient. Additional aspects related to each phaseof the workflow 100 are provided below in greater detail. Step 110 ofthe workflow 100 represents image acquisition and non-invasivemeasurements at a rest state of the patient. The image acquisition maybe acquired with a CT scan, an MRI scan, an angiography scan, anultrasound scan, a cardiac perfusion scan, or other technology capableof obtaining an accurate, clear image of a patient's anatomicalframework. The non-invasive measurements may include, but are notlimited to, heart rate and blood pressure.

At 120, anatomical modeling is performed to derive a framework based onthe anatomical model of the coronary tree for the patient. Theanatomical modeling may include establishing parameters with respect tothe acquired image of the patient, such as, for example, flow andpressure through various portions of the coronary tree. The anatomicalmodeling may also include segmenting the coronary tree to focus on areasof concern for the particular patient. The anatomical modeling mayinvolve constructing a 3D model of the patient's coronary vessels, theproximal aorta, and the myocardium.

Step 130 of the workflow 100 represents a clinician's input, includingproviding feedback to the anatomical model to adjust the model based onhis or her knowledge or other information related to the patient, forexample.

Flow computations are computed at 140, with feedback from the clinician(130 of the workflow 100) being inputted as necessary, to arrive at thefunctional assessment of the patient's coronary tree. The flowcomputations use hyperemic boundary conditions, which are adjusted as aresult of applying a feedback control system that performs a simulationmatching the rest state. The feedback control system utilizes a modelbased on the anatomical model of the coronary tree, and also includes aplurality of controllers, with each of the plurality of controllersrelating to a respective output variable of the coronary tree. The modelis adjusted to allow for the output variables to be in agreement withthe rest state measurements. The output variables agreeing with the reststate measurements is an indication that the model accurately reflectsthe patient. Then, the hyperemic boundary conditions are adjusted basedon the adjustments made to the model. The feedback control system isdescribed in greater detail with respect to FIGS. 4, 5A, and 5B.

A report is provided at 150, with the report identifying results of asimulation corresponding to the hyperemic state using the adjustedmodel. The report includes the functional assessment of the patient'scoronary tree and may include, but is not limited to, such informationas fractional flow reserve (FFR) and coronary flow reserve (CFR)parameters based on the hyperemic state that serve as importantdiagnostic tools for a physician.

For an accurate simulation of a patient's coronary blood-flow, two keyrequirements for computational fluid dynamics (CFD)-based methods are(1) an anatomical model of the coronary vessel tree and (b) the boundaryconditions at the inlet and outlets. Recent advances in medical imageprocessing have addressed the former by employing manual, semi-automaticor fully-automatic algorithms for multi-modality image segmentation andsurface mesh generation.

FIG. 2 provides a representation 200 for estimating boundary conditionsat the rest state, while FIG. 3 provides a representation 300 of theestimation of boundary conditions at the hyperemic state, both of whichare more fully described below.

Estimation of Boundary Conditions at Rest State

Since the region of interest, namely the coronary vessel tree, is partof the larger circulation system, the inlet and outlet boundaryconditions are chosen such that they adequately model the proximal anddistal phenomenon of the patient's circulation. The models take intoaccount the effect of the myocardial contraction on the flow. Theselumped models are usually composed of a set of resistances andcompliances, which represent the micro-vascular beds. The complianceinfluences the transient waveform, while the mean value is affected onlyby the resistance. Since the key diagnostic indexes (such as FFR andCFR) are based on average quantities over the cardiac cycle, theboundary condition estimation is limited to correctly determining theresistance values at each outlet, which is defined as the ratio of thepressure to the flow through that outlet. Mean arterial pressure (MAP)is constant in healthy epicardial arteries and can be estimated bysystolic, diastolic cuff blood pressures (SBP and DBP), and the heartrate as follows:MAP=DBP+[⅓+(HR×0.0012)](SBP−DBP).

Coronary flow depends on the oxygen demand of the heart, and sinceoxygen extraction in the coronary capillaries is close to maximum levelseven at rest state, the increased metabolic need can be satisfied onlythrough an increased flow, hence coronary flow is proportional to theoxygen demand. It is difficult to quantify oxygen demand and consumptionin the coronaries through non-invasive measurements. Several methods forestimating oxygen consumption from mechanical variables have beenproposed in the past, with heart rate as a primary determinant of oxygenconsumption. The second major determinant is pressure (pressuregeneration costs more oxygen than muscle shortening, i.e. flow). Themost widely used index for estimating the myocardial oxygen consumptionis the rate-pressure product, according to which:

$\begin{matrix}{q_{rest} = {8 \times \left\{ {\left\lbrack {7 \times 10^{- 4}\left( {{HP} \cdot {SBP}} \right)} \right\rbrack - 0.4} \right\}{\frac{ml}{\min}/100}\mspace{14mu}{g.}}} & (1)\end{matrix}$

To determine the absolute value of resting flow (Q_(rest)), restingperfusion is multiplied with total myocardial mass. In normal hearts,the left ventricle typically represents two-thirds of the total mass,i.e. Q_(rest)=q_(rest)×1.5×M_(LV). Hence total coronary resistance canbe computed as R_(cor)=MAP/Q_(rest). The value M_(LV) is estimated fromCT images by myocardial segmentation. The next step is to distribute thetotal resistance to the various lumped models at the outlets. To dothis, Murray's law, which states that the energy required for blood flowand the energy needed to maintain the vasculature is assumed minimal andhence, Q_(i)˜k r_(i) ³, where k is a constant and r is the radius of thevessel. A value of 3 for the power coefficient has been suggestedthrough the observed invariability of wall shear stress (rate) when flowrate varies substantially. Next, the absolute resting flow, which is thesum of all outlet flows, is written as:Q+rest=Σ_(i=1) ^(n) k·r _(i) ³=Σ_(i=1) ^(n) Q _(i).

The flow through a particular outlet is determined by:

$\begin{matrix}{\frac{Q_{i}}{Q_{rest}} = {{\frac{k \cdot r_{i}^{3}}{\sum\limits_{j = 1}^{n}{k \cdot r_{j}^{3}}}->Q_{i}} = {Q_{rest} \cdot {\frac{r_{i}^{3}}{\sum\limits_{j = 1}^{n}r_{j}^{3}}.}}}} & (2)\end{matrix}$

Therefore, the terminal resistances can now be determined by:

$\begin{matrix}{R_{i} = {\frac{MAP}{Q_{i}} = {{MAP} \cdot {\frac{\sum\limits_{j = 1}^{n}r_{j}^{3}}{Q_{rest} \cdot r_{i}^{3}}.}}}} & (3)\end{matrix}$

Referring to FIG. 2, the representation 200 provides a concise summaryof the estimation of boundary conditions at the rest state, as describedabove with respect to equations (1), (2), and (3). The input parameters210 used for the estimation include heart rate, diastolic bloodpressure, systolic blood pressure, and the image data (such as CT imagedata). Boundary condition estimation at rest (220) is performed with theinput parameters 210 and the equations (1), (2), and (3), resulting inthe coronary bed and systemic circulation boundary conditions at rest(230). The boundary conditions at rest include, but are not limited to,the rate-pressure product, q_(rest); the flow through a particularoutlet, Q_(i); and terminal resistances, R_(i).

Estimation of Boundary Conditions at Hyperemia

Intracoronary and intravenously drug-induced hyperemia leads to similardecreases in micro-vascular resistances. The intravenous administrationof adenosine leads to a slight increase of heart rate and decrease ofblood pressure. For a simulation the effect of intracoronary vasodilatorcan be extended infinitely and it minimally influences the heart rateand blood pressure. Adenosine leads to an increase in coronary flowvelocity of around 4.5 for normal, healthy subjects (with no coronaryartery disease). Since blood pressure decreases slightly duringhyperemia, a 4.5-fold increase in flow does not mean a 4.5-fold decreasein coronary resistance. A total coronary resistance index (TCRI) can becomputed, which is equal to:

$\begin{matrix}{{TRCI} = {\left( {\frac{{MAP}_{hyper}}{Q_{hyper}}/\frac{{MAP}_{rest}}{Q_{rest}}} \right) = {\frac{\left( R_{cor} \right)_{hyper}}{\left( R_{cor} \right)_{rest}}.}}} & (4)\end{matrix}$

A mean value of TCRI=0.22 has been obtained during various studies. Itincreases from 0.22, for HR less than 75 bpm, to 0.26, for a heart rateof 100 bpm, and to 0.28 for a heart rate of 120 bpm. Therefore, thefollowing relationship can be derived to obtain a HR corrected TCRI:

${TRCI}_{corr} = \left\{ {\begin{matrix}{{0.0016 \cdot {HR}} + 0.1} & {{{{for}\mspace{14mu}{HR}} \leq {100\mspace{14mu}{bpm}}};} \\{{0.001 \cdot {HR}} + 0.16} & {{{for}\mspace{14mu}{HR}} > {100\mspace{14mu}{bpm}}}\end{matrix}.} \right.$

Finally, hyperemic micro-vascular resistances are computed by:(R _(i))_(hyper)=(R _(i))_(rest)·TCRI  (5).

(R_(i))_(rest) is the value from equation (3).

Referring to FIG. 3, the representation 300 provides a concise summaryof the estimation of boundary conditions at hyperemia, as describedabove with respect to equations (4) and (5). The input parameters 210and the boundary condition estimation at rest state 220 are applied to amodel for effect of hyperemia 310, as represented by equations (4) and(5). This results in the coronary bed and systemic circulation boundaryconditions at hyperemia (320). The boundary conditions at hyperemiainclude, but are not limited to, total coronary resistance index, TCRI;and hyperemic micro-vascular resistances, (R_(i))_(hyper).

Feedback Control System

In order to accurately evaluate coronary diagnostic indexes, the goal ofa CFD simulation is to obtain the same average pressure and flow ratesinside the coronary arteries as that of obtained if the patient were inthe rest/drug-induced intracoronary hyperemia. Since the proposed methodis based on parameters acquired during the rest state, it is importantto first set-up the simulation for the rest state and then make thetransition to the hyperemia. The coronary resistances are determined asdescribed above with respect to the description of the estimation ofboundary conditions at rest state. As a result, if the simulated MAPmatches the value determined through equation (1), the coronary flowautomatically matches the estimated value. During intracoronarydrug-induced hyperemia, MAP drops slightly due to the decrease incoronary resistances. To capture this aspect, the coronary tree iscoupled to the aorta. This coupling also enables the use of a simplifiedheart model in order to provide the inlet boundary condition. If onlythe coronaries were modeled, then either time-varying flow or pressurewould be needed at inflow, none of which is available non-invasively.Coronary flow at rest represents around 4-5% of the total cardiacoutput. Although the focus lies on the coronary circulation, thesystemic resistances (coupled at the outlet of the aorta and of theother proximal vessels) are adapted so that the total coronary flow isaround 4-5% of the cardiac output. The second reference variable is thecoronary flow as a percent of the cardiac output. An accurate estimatefor it during rest is important to obtain an accurate decrease in aorticpressure when performing simulation at hyperemia.

FIG. 4 displays the feedback control system 400 that is used for therest state estimation and for the flow computations for the hyperemicstate. The feedback control system utilizes a model 430 based on theanatomical model of the coronary tree and includes a plurality ofcontrollers (such as controllers 410 and 420), each of which correspondsto a respective output variable of the coronary tree. As shown, thecontroller 410 is a systemic resistance controller relating to coronaryresistance of the coronary tree, and the controller 420 is a cardiacoutput controller relating to the cardiac output. The systemicresistance controller is a Proportional Integral (PI) controller, whilethe cardiac output controller is a Proportional Integral Derivative(PID) controller. The patient model 430 (i.e., the anatomical model ofthe coronary tree for the patient) is used to generate simulated valuesof flow and pressure. The simulated values are adapted into the flowcomputation equations (computations 440 and 450), the results of whichare compared to those derived from the non-invasive measurements. If anerror (E) is determined to exist from the comparison, the controllers410 and 420 adjust parameters of the model 430 to allow for the outputvariables to be in agreement with the rest state measurements. Thisprocess may take several iterations until the model 430 accuratelyreflects the patient. Moreover, additional controllers (not shown) mayalso be incorporated into the feedback control system 400. If included,each additional controller relates to another aspect of the coronaryvessel tree and may increase the accuracy of the patient model 430.

Once the output variables are in agreement with the variables based onthe non-invasive measurements, the hyperemic boundary conditions areaccordingly adjusted based on adjustments made to the patient model 430and are used in the flow computation equations to obtain the coronarycirculation parameters (flow and pressure) during the hyperemic statefor the patient.

This process is further represented in the flow diagram 500 of FIG. 5Aand the computation representation 570 of FIG. 5B. With reference toFIG. 5A, at 510, model parameters are initialized. This refers to thesimulated values of flow and pressure, for example. At 520, flowcomputations are performed. At 530, a comparison is done between themeasured data (based on the non-invasive measurements) and the simulateddata (based on the model). At 540, a determination is made to establishif an objective is satisfied. The objective may refer to a percent errorbetween the measured data and the simulated data. If the percent erroris less than or equal to a predetermined value (which may be differentfor each variable), then the objective is satisfied. At 550, if thepercent error is not less than the predetermined value, then the modelparameters need to be updated as determined by the controllers 410 and420. The computations at 520, the evaluation at 530, and thedetermination of satisfying the objective at 540 are repeated. Once theobjective is satisfied, the results may be reported at 560.

FIG. 5B illustrates the computational process 570 that leads to thecoronary circulation parameters (flow and pressure) during the hyperemicstate for the patient. Flow computations (590), using the boundaryconditions at hyperemia (320) along with a model of the heart (575) andthe patient's model (580, 585), are used to derive the coronary flow andcoronary pressure at hyperemia (595). These parameters may be used todetermine other hyperemic variables for the patient.

From a sensitivity analysis, there are various ways to change thecardiac output of the heart model, namely the time of maximum elastance,maximum contractility, dead volume, initial left ventricle (LV) volume,systemic resistance or left atrial pressure (heart rate is given andcannot be changed). The highest sensitivity is due to the differencebetween initial LV volume and dead volume. Note that the goal of theproposed method is to reach a steady-state which matches thepatient-specific steady-state correctly, and not necessarily model thetransient aspects of the control mechanism. Once the simulation hasconverged and the values for the systemic resistances and for thedifference between initial LV volume and dead volume have beendetermined, the control loop is switched off, and the rest outletresistances are substituted by the hyperemic resistances. Thus the MAPis allowed to drop slightly and the percentage represented by thecoronary flow out of the total flow becomes much higher since coronaryflow increases several times. The simulation is run again untilconvergence.

FIG. 6 provides a representation 600 of a model of the coronarycirculation, indicating the points of boundary conditions labeled as“BC”. Ra indicates the proximal arterial resistance; Ca the arterialcompliance; Ram microvascular arterial resistance; Cim intra-myocardialcompliance (which accounts for volume reduction at systoliccontraction); Rvm microvascular venous resistance; and Rv venousresistance.

The method described herein has been tested using a reduced-orderpatient-specific model. The proximal vessels are modeled using IDsegment while the micro-vascular beds are represented either through3-element Windkessel models, or through specialized lumped models forthe coronary circulation. The total outflow resistances have beendetermined, while the lumped coronary models are composed of fourdifferent resistances. The first resistance is equal to thecharacteristic resistance in order to minimize the reflections, whilethe third and fourth resistances represent the micro-vascular venous andvenous resistances which are considered constant. Thus themicro-vascular arterial resistance is determined as difference betweenthe total and the three other resistances. Note that the averagepressure and flow depend on total resistance and not on its distributionto the individual resistances. Patient-specific data was extracted fromCoronary CTA scans by image segmentation, centerline and lumenextraction. The systemic circulation is represented by average lengthsand radiuses, but this does not affect the results since the role of thesystemic circulation is to correctly capture the hyperemic conditionsand this goal is achieved if the rest state pressure and the percentageof coronary flow match the patient-state. An artificial 65% diameterstenosis with a length of 1.0 cm has been introduced on one of the leftdescending artery branches. A sensitivity analysis has been performedfor the four different input parameters of the proposed method: heartrate, systolic and diastolic pressure (taken together since the MAP isthe actual input), the left ventricular mass and the power coefficientn. The base values used for the analysis are: HR=60 bpm, SBP=140 mmHg,DBP=100 mmHg, LVM=250 gm, n=3. Each input parameter is variedindividually by ±10%, ±20% and ±30% (except the power coefficient, whereonly ±10% and ±20% variations were done). The cuff pressures were variedsimultaneously by the same percentage.

FIGS. 7A and 7B show the results, respectively 710 and 720, of thesensitivity analysis for the trans-stenotic pressure drop (P) and Pd/Pa.The highest sensitivity for P is with respect to the cuff-pressures,followed by LVM (see 710 in FIG. 7A). For FFR (Pd/Pa), the highestsensitivity is with respect to the LVM, followed by HR (see 720 in FIG.7B). In both cases, the power coefficient has minimal influence. Tofurther demonstrate the need for accurate outlet boundary conditionestimation, the hyperemic resistances have been directly manipulated by±10%, ±20% and ±30% and Table I below displays the results for ΔP andFFR. The results clearly show that is not sufficient to use a controlloop as the one depicted in FIG. 4, or any other approach, which matchesthe heart rate and the pressure of the patient, but it is crucial tocorrectly determine the rest and hyperemic micro-vascular resistance ofeach outflow vessel, in order to correctly estimate the values ofhemodynamic indexes. For the given case, FFR value varies between 0.628and 0.784, an interval which intersects the cut-off value used inclinical practice.

TABLE I R_(hyper) P_(a) P_(d) Q ΔP P_(d)/P_(a)  7579 (−30%) 100.01 62.792.11 37.22 0.628  8661 (−20%) 101.64 67.55 1.99 34.09 0.664  9744 (−10%)102.97 71.67 1.88 31.30 0.696 10827 (0%)  104.01 75.21 1.77 28.80 0.72311919 (+10%) 105.03 78.40 1.68 29.80 0.746 12993 (+20%) 105.83 81.171.60 24.66 0.766 14076 (+30%) 106.54 83.62 1.52 22.92 0.784

FIGS. 8A-8D display the evolution of the two controlled variables(aortic pressure (810 in FIG. 8A) and the percentage of coronary flow(820 in FIG. 8B)) and of the system inputs (systemic resistance (840 inFIG. 8D) and initial LV volume (830 in FIG. 8C)) during a simulationperformed with the base values of the parameters. Each plot is dividedinto three sections: (1) represents the initialization period, (2)represents the period of time during which the feedback control systemdisplayed in FIG. 4 is used and the rest state is simulated, and (3)represents the simulation of the hyperemic state. FIGS. 8A and 8Bclearly show how, during phase (2) of the simulation, the valuesconverge to the reference values estimated for the rest state of thepatient. During phase (3) (hyperemia), the two system inputs remainconstant (the feedback loops is no longer used), and, since the coronaryresistance decreases, the aortic pressure decreases and the percentagecoronary flow increases.

A method is introduced for estimating patient-specific coronary boundaryconditions (at rest and hyperemia) together with a feedback controlsystem which can be used to ensure that a CFD-based simulation matchesthe patient-specific coronary pressure and flow. The main advantages ofthis approach are that it is based solely on parameters, which areacquired non-invasively during the rest state, and that it can be usedfor full-order or reduced-order simulations. Further, it can be used toassess coronary diagnostic indexes which are based solely on thehyperemic state (e.g., FFR) or based on both rest and hyperemic state(e.g., CFR).

The proposed method does not take into consideration differences betweengenders (women require a higher resting flow for a similar amount ofmyocardial mass), but there is no study which also takes into accountthe gender when assessing resting coronary flow. Patients with restangina have to be excluded, since angina means that rest flow does notmatch the oxygen demand, therefore equation (1) may no longer be valid.Hypertensive patients and patients with micro-vascular disease have tobe modeled separately, since the TCRI values computed through equation(4) would be no longer valid.

The feedback control system 400 may be one or more processing devices,computing devices, processors, or the like for performing calculationsand operations described herein. For example, one or more processors maybe used to perform the calculations and operations of determining therest state and hyperemic state boundary conditions, implementing thepatient model 430 and the controllers 410 and 420, and determining theflow computations.

The feedback control system 400 may interface with one or more memorydevices (not shown) such as read only memory (ROM), random access memory(RAM), and one or more optional non-transitory memory devices such as,for example, an external or internal DVD drive, a CD ROM drive, a harddrive, flash memory, a USB drive, or the like. The memory devices may beconfigured to include individual files and/or one or more databases forstoring any software modules, instructions, or data.

Program instructions, software, or interactive modules for performingany of the functional steps associated with the processes as describedabove may be stored in the ROM and/or the RAM. Optionally, the programinstructions may be stored on a tangible computer readable medium suchas a compact disk, a digital disk, flash memory, a memory card, a USBdrive, an optical disc storage medium, such as a Blu-Ray™ disc, and/orother recording medium.

An optional display interface may permit information from the feedbackcontrol system 400 to be displayed on one or more displays in audio,visual, graphic, and/or alphanumeric format. Communication with externaldevices may occur using various communication ports that may be attachedto one or more communications networks, such as the Internet or a localarea network, or directly to a portable computing device such as anotebook computer. An interface may allow for receipt of data from inputdevices such as a keyboard, a mouse, a joystick, a touch screen, aremote control, a pointing device, a video input device, an audio inputdevice, and the like.

Although the present invention has been described with reference toexemplary embodiments, it is not limited thereto. Those skilled in theart will appreciate that numerous changes and modifications may be madeto the preferred embodiments of the invention and that such changes andmodifications may be made without departing from the true spirit of theinvention. It is therefore intended that the appended claims beconstrued to cover all such equivalent variations as fall within thetrue spirit and scope of the invention.

We claim:
 1. A method of non-invasively determining coronary circulationparameters during a hyperemic state for a patient, the methodcomprising: obtaining an image of an anatomical framework of the patientthrough an image acquisition device; obtaining an anatomical model of acoronary tree of the patient based on the anatomical image; determiningrest boundary conditions of the patient based on non-invasivemeasurements taken at a rest state, wherein the rest boundary conditionsinclude a rate-pressure product, a flow through a particular vesseloutlet, and terminal resistances; computing hyperemic boundaryconditions of the patient, wherein the hyperemic boundary conditions ofthe patient are a product of a total coronary resistance index and therest boundary conditions of the patient; adjusting the anatomical modelto match the rest state by iteratively generating simulated values offlow and pressure until the simulated values match the rest boundaryconditions, wherein parameters of the anatomical model are adjustedduring each iteration using a plurality of controllers, each controllercorresponding to a different output variable of the coronary tree;wherein a first controller of the plurality of controllers is aProportional Integral (PI) controller that calculates coronaryresistance of the coronary tree, and wherein a second controller of theplurality of controllers is a Proportional Integral Derivative (PID)controller that calculates a difference between an initial leftventricle volume and a dead volume; adjusting the hyperemic boundaryconditions based on the adjustments to the anatomical model; performinga flow computation corresponding to the hyperemic state using theadjusted anatomical model; and providing a report identifying one ormore results of the flow computation that includes a functionalassessment of the patient's coronary tree and coronary flow reserveparameters.
 2. The method of claim 1, wherein the anatomical model ofthe coronary tree of the patient is obtained via at least one of a CTscan, an MRI scan, an angiography scan, an ultrasound scan, and acardiac perfusion scan.
 3. The method of claim 1, wherein thenon-invasive measurements taken at a rest state comprise one or more ofheart rate, systolic blood pressure, and diastolic blood pressure. 4.The method of claim 1, wherein the rest boundary conditions of thepatient comprise terminal resistance and capacitance values at vesseloutlets during the rest state.
 5. The method of claim 4, wherein therest boundary conditions of the patient based on the terminal resistanceand capacitance values at vessel outlets during the rest state areadjusted using information from a cardiac perfusion exam.
 6. The methodof claim 1, wherein the hyperemic boundary conditions of the patientbased on the terminal resistance and capacitance values at vesseloutlets during the hyperemic state are adjusted using information from acardiac perfusion exam.
 7. A feedback control system for non-invasivelydetermining coronary circulation parameters during a hyperemic state fora patient, the system comprising: one or more processors configured tocalculate (i) rest boundary conditions of the patient based onnon-invasive measurements taken at a rest state, wherein the restboundary conditions include a rate-pressure product, a flow through aparticular vessel outlet, and terminal resistances; and (ii) hyperemicboundary conditions of the patient, wherein the hyperemic boundaryconditions of the patient are a product of a total coronary resistanceindex and the rest boundary conditions of the patient; wherein the oneor more processors are further configured to: adjust an anatomical modelprovided based on an anatomical image, to match the rest state byiteratively generating simulated values of flow and pressure until thesimulated values match the rest boundary conditions, wherein parametersof the anatomical model are adjusted during each iteration using aplurality of controllers each controller corresponding to a differentoutput variable of the coronary tree; wherein a first controller of theplurality of controllers is a Proportional Integral (PI) controller thatcalculates coronary resistance of the coronary tree, and wherein asecond controller of the plurality of controllers is a ProportionalIntegral Derivative (PID) controller that calculates a differencebetween an initial left ventricle volume and a dead volume; wherein theone or more processors are further configured to: adjust the hyperemicboundary conditions based on the adjustments to the parameters of theanatomical model; and perform a flow computation corresponding to thehyperemic state using the adjusted anatomical model; wherein the one ormore processors are further configured to: provide a report identifyingone or more results of the flow computation that includes a functionalassessment of the patient's coronary tree and coronary flow reserveparameters.
 8. The system of claim 7, wherein the anatomical model ofthe coronary tree of the patient is obtained via at least one of a CTscan, an MM scan, an angiography scan, an ultrasound scan, and a cardiacperfusion scan.
 9. The system of claim 7, wherein the non-invasivemeasurements taken at a rest state comprise one or more of heart rate,systolic blood pressure, and diastolic blood pressure.
 10. The system ofclaim 7, wherein the rest boundary conditions of the patient compriseterminal resistance and capacitance values at vessel outlets during therest state.
 11. A non-transitory computer-readable media comprisingsoftware instructions for non-invasively determining coronarycirculation parameters during a hyperemic state for a patient by:obtaining an image of an anatomical framework of the patient through animage acquisition device; obtaining an anatomical model of a coronarytree of the patient based on the anatomical image; determining restboundary conditions of the patient based on non-invasive measurementstaken at a rest state, wherein the rest boundary conditions include arate-pressure product, a flow through a particular vessel outlet, andterminal resistances; computing hyperemic boundary conditions of thepatient, wherein the hyperemic boundary conditions of the patient are aproduct of a total coronary resistance index and the rest boundaryconditions of the patient; adjusting the anatomical model to match therest state by iteratively generating simulated values of flow andpressure until the simulated values match the rest boundary conditions,wherein parameters of the anatomical model are adjusted during eachiteration using a plurality of controllers each controller correspondingto a different output variable of the coronary tree; wherein a firstcontroller of the plurality of controllers is a Proportional Integral(PI) controller that calculates coronary resistance of the coronarytree, and wherein a second controller of the plurality of controllers isa Proportional Integral Derivative (PID) controller that calculates adifference between an initial left ventricle volume and a dead volume;adjusting the hyperemic boundary conditions based on the adjustments tothe anatomical model; performing a flow computation corresponding to thehyperemic state using the adjusted anatomical model; and providing areport identifying one or more results of the flow computation thatincludes a functional assessment of the patient's coronary tree andcoronary flow reserve parameters.
 12. The non-transitorycomputer-readable media of claim 11, wherein the non-invasivemeasurements taken at a rest state comprise one or more of heart rate,systolic blood pressure, and diastolic blood pressure.
 13. Thenon-transitory computer-readable media of claim 11, wherein the restboundary conditions of the patient comprise terminal resistance andcapacitance values at vessel outlets during the rest state.